Stoke struggled to get into gear in the opening 45 minutes and despite creating the better of the chances after the interval, failed to find a leveller at Selhurst Park.
Hughes made eight changes to his side as Wilfried Zaha's first-half strike settled the tie at Selhurst Park.
It was the second cup exit in a matter of days following the Potters' heartbreaking loss to Liverpool in the Semi-Final of the Capital One Cup.
"It's been a difficult week for us all this week to be perfectly honest," the Welshman said to Stoke City Player.
"Today was a disappointing result, because this is a competition that we wanted to progress and do well in.
"On the day we had a decent amount of possession and approach play but never produced that one ball or clear cut chance.
"For the most part I thought we were the better team, particularly for the football we produced but that was only up to a point and we couldn't get that end product when we needed it.
"It's a shame because in the first half the one real chance they created was our mistake on the edge of the box when we needed to be more stronger.
"I can't fault the players' effort, they gave it a real go, but we just lacked that quality that we needed."
With captain Ryan Shawcross still out of action, Hughes has gained another defensive concern after Marc Wilson suffered an injury toward the end of the tie.
The Republic of Ireland international suffered the setback following a challenge in second half stoppage time and had to be carried off at the final whistle.
"We're a little bit weakened at the back at the moment," he added.
"It may be a little bit too soon to say what he's done but the fear is he has a ligament injury and we could be looking at 10-12 weeks out at the moment.
"That's all depending on whether the cruciate is ok, so we will have to check him to gain a clear idea on the seriousness of it."